On Anomaly Ranking and Excess-Mass Curves

Nicolas Goix, Anne Sabourin, Stéphan Clémençon
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:287-295, 2015.

Abstract

Learning how to rank multivariate unlabeled observations depending on their degree of abnormality/novelty is a crucial problem in a wide range of applications. In practice, it generally consists in building a real valued "scoring" function on the feature space so as to quantify to which extent observations should be considered as abnormal. In the 1-d situation, measurements are generally considered as ”abnormal” when they are remote from central measures such as the mean or the median. Anomaly detection then relies on tail analysis of the variable of interest. Extensions to the multivariate setting are far from straightforward and it is precisely the main purpose of this paper to introduce a novel and convenient (functional) criterion for measuring the performance of a scoring function regarding the anomaly ranking task, referred to as the Excess-Mass curve (EM-curve). In addition, an adaptive algorithm for building a scoring function based on unlabeled data with a nearly optimal EM is proposed and is analyzed from a statistical perspective.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-goix15, title = {{On Anomaly Ranking and Excess-Mass Curves}}, author = {Goix, Nicolas and Sabourin, Anne and Clémençon, Stéphan}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {287--295}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/goix15.pdf}, url = {https://proceedings.mlr.press/v38/goix15.html}, abstract = {Learning how to rank multivariate unlabeled observations depending on their degree of abnormality/novelty is a crucial problem in a wide range of applications. In practice, it generally consists in building a real valued "scoring" function on the feature space so as to quantify to which extent observations should be considered as abnormal. In the 1-d situation, measurements are generally considered as ”abnormal” when they are remote from central measures such as the mean or the median. Anomaly detection then relies on tail analysis of the variable of interest. Extensions to the multivariate setting are far from straightforward and it is precisely the main purpose of this paper to introduce a novel and convenient (functional) criterion for measuring the performance of a scoring function regarding the anomaly ranking task, referred to as the Excess-Mass curve (EM-curve). In addition, an adaptive algorithm for building a scoring function based on unlabeled data with a nearly optimal EM is proposed and is analyzed from a statistical perspective.} }
Endnote
%0 Conference Paper %T On Anomaly Ranking and Excess-Mass Curves %A Nicolas Goix %A Anne Sabourin %A Stéphan Clémençon %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-goix15 %I PMLR %P 287--295 %U https://proceedings.mlr.press/v38/goix15.html %V 38 %X Learning how to rank multivariate unlabeled observations depending on their degree of abnormality/novelty is a crucial problem in a wide range of applications. In practice, it generally consists in building a real valued "scoring" function on the feature space so as to quantify to which extent observations should be considered as abnormal. In the 1-d situation, measurements are generally considered as ”abnormal” when they are remote from central measures such as the mean or the median. Anomaly detection then relies on tail analysis of the variable of interest. Extensions to the multivariate setting are far from straightforward and it is precisely the main purpose of this paper to introduce a novel and convenient (functional) criterion for measuring the performance of a scoring function regarding the anomaly ranking task, referred to as the Excess-Mass curve (EM-curve). In addition, an adaptive algorithm for building a scoring function based on unlabeled data with a nearly optimal EM is proposed and is analyzed from a statistical perspective.
RIS
TY - CPAPER TI - On Anomaly Ranking and Excess-Mass Curves AU - Nicolas Goix AU - Anne Sabourin AU - Stéphan Clémençon BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-goix15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 287 EP - 295 L1 - http://proceedings.mlr.press/v38/goix15.pdf UR - https://proceedings.mlr.press/v38/goix15.html AB - Learning how to rank multivariate unlabeled observations depending on their degree of abnormality/novelty is a crucial problem in a wide range of applications. In practice, it generally consists in building a real valued "scoring" function on the feature space so as to quantify to which extent observations should be considered as abnormal. In the 1-d situation, measurements are generally considered as ”abnormal” when they are remote from central measures such as the mean or the median. Anomaly detection then relies on tail analysis of the variable of interest. Extensions to the multivariate setting are far from straightforward and it is precisely the main purpose of this paper to introduce a novel and convenient (functional) criterion for measuring the performance of a scoring function regarding the anomaly ranking task, referred to as the Excess-Mass curve (EM-curve). In addition, an adaptive algorithm for building a scoring function based on unlabeled data with a nearly optimal EM is proposed and is analyzed from a statistical perspective. ER -
APA
Goix, N., Sabourin, A. & Clémençon, S.. (2015). On Anomaly Ranking and Excess-Mass Curves. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:287-295 Available from https://proceedings.mlr.press/v38/goix15.html.

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